Can You Solve the Equation 5^n = 80n for n?

[One-D]

I've got a problem with this:
5^n=80n
find n!
I can't solve out this one.
thanx for ur help, I'm not sure if it's the right place for this thread.

 

[Berislav]

If n \in \mathbb{Z}, there is no such number.

 

[cronxeh]

5^x - 80*x = 0
plot it
and so far I've found 2 solutions (oh and there are no solns in Z of course)

Approximate roots are:

n=0.012759
n=3.50133

 

[Zurtex]

Anyway the 2 exact solutions (in real numbers) are:

n = -\frac{\text{ProductLog} \left( - \frac{\ln 5}{80} \right)}{\ln 5}

and

n = -\frac{\text{ProductLog} \left(-1, - \frac{\ln 5}{80} \right)}{\ln 5}

Which works out to 100 sf.:

n = 0.01275934595849510712320293028417381446823346765193827957982622843955432250672941443435143426214944153

And:

n = 3.501327193786496727104387840526356291207393167955463046140101380079871277483867981890189846055191784

 

[cronxeh]

and that is an 'analytical' solution?

 

[One-D]

thanx for ur replies